Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient

The nature of the singular ®eld around the crack in functionally graded material (FGM) is analyzed parametrically using ®nite element method. The numerical simulations are carried out by varying the location of the crack in the graded region for di€erent material gradients. Using linear material property variation in the gradient zone, the in¯uence of material gradient and the crack position on the fracture parameters such as complex stress intensity factor (SIF) and energy release rate are studied. The crack opening displacement pro®les of FGM are compared with the homogeneous and bimaterial counterparts. The analysis shows that the fracture parameters of FGM approach that of the bimaterial as the material gradient is increased, regardless of the position of the crack in the graded region. The extent of applicability of the homogenous crack tip ®elds around the crack in FGM is analyzed, and the results show that the size of the homogeneous ®eld reduces with the increase in material gradient. Static fracture experiments are conducted on epoxy based FGM to determine complex SIF with electrical strain gages, using the homogeneous ®eld equations to convert the strains to SIF. The measured SIF values compare favorably with the numerical results providing a limited experimental validation of the computations and the use of homogeneous ®eld for FGM. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Functionally graded